A formal series of the form \begin{equation*} \sum_{n=m}^\infty a_n z^{n/k} \end{equation*}where $m$ and $k$ are integers such that $k \geq 1$ is is called a Puiseux series or a fractional power series. Note that if $k > 1$ then $z^{n/k}$ could be multivalued. One example of the use of such a power series is the Puiseux parametrization of one-dimensional complex analytic varieties.

Bibliography

1

E. M. Chirka. Complex Analytic Sets. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1989.

2

Alexandru Dimca. Topics on Real and Complex Singularities. Vieweg, Braunschweig, Germany, 1987.